Learn Turkish: Siz on beş mühendissiniz. - You are fifteen engineers.

You simply put the word for ten (on) followed by the single digit, with a space in between. So, fifteen is on (ten) plus beş (five), written as two separate words: on beş.

Since there are fifteen engineers, shouldn't the noun be plural (mühendisler)?

No, and this is a very important rule in Turkish! Whenever you use a specific number before a noun, the noun itself must stay in the singular form. So it is always on beş mühendis, never on beş mühendisler.

What does the -siniz at the end of mühendissiniz do?

It is the personal suffix for siz (you, plural or formal). Because Turkish doesn't have a separate word for "are" in simple present sentences, you attach -siniz directly to the noun to mean "you are".

Why does the suffix take the form -siniz instead of -sunuz?

This happens because of 4-way vowel harmony. The suffix changes to match the last vowel of the word it attaches to. The last vowel in mühendis is i. According to the rules, if the last vowel is e or i, the suffix will use i, making it -siniz.